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You have now had a number of opportunities to consider what it looks like to incorporate the disciplinary literacy practices of reading, writing, speaking, and listening into mathematics classrooms. As a way to revisit what it means to engage in these disciplinary literacy practices, solve the Harvesting the Field Problem [PDF], drawing on the strategies and protocols you have explored so far as you work toward a solution.

**Apply**: Write your thoughts on the following questions:

- How did you make sense of what this problem was asking? What strategies and protocols helped you do this? What did you learn from using these strategies and protocols?
- Once you made sense of the problem, how did you solve it? Did you make notes, draw a diagram, or create some equations? Did you try possible solutions to see if they worked? Did you wonder if there might be more than one possible solution? How did your solution efforts compare to what you saw students doing as they solved problems in the videos you viewed?
- Once you solved the problem, consider how you would have explained your solution to someone else. What would be important to explain? How would you use words, diagrams, and equations to communicate your explanation in writing? How might your written explanation have compared to the mathematical writing in the videos you viewed?
- Imagine that you had been able to work on this problem with a friend or colleague. How would a conversation about what the problem was asking have helped? How would sharing and discussing your initial efforts to solve the problem have helped? How would articulating your solutions to each other have helped? How might your imaginary conversation compare to how you saw students speaking and listening together in the videos you viewed?

This unit is intended to address what it means to plan, teach, and reflect on mathematics lessons that provide *all* students with opportunities to engage in the disciplinary literacy practices associated with mathematics. The Harvesting the Field problem was intended to engage you in these practices. How would you plan, teach, and reflect on mathematics lessons that engaged your own students in these practices?

**Video and Reflection:** Watch *Reading and Writing in Mathematics *to see an example of how disciplinary literacy practices are brought together in the study of mathematics. You may want to take notes on the questions below.

**Before you watch:**How does reading, writing, speaking, and listening provide opportunities to engage in the authentic work of mathematicians? How does this support mathematics learning? What are the implications for how you plan for instruction?**Watch the video:**As you watch, notice how reading, writing, speaking, and listening are framed in this video. What new ideas surface for you as you contemplate implications for instruction?**Reflect:**How similar or different are the practices discussed in this video compared to the practices in your own classroom? What new ideas might be important to begin to implement in your own classroom, and why?

If mathematics classrooms were to be designed to strengthen and support student engagement in disciplinary literacy practices that are consistent with the expectations of the Common Core State Standards for Mathematics (CCSSM), including the Standards for Mathematical Practice, what would mathematics lessons need to look like? Here are some components that might be important:

- Rich non-routine problems or tasks addressing the mathematics students are expected to learn.
- Students working together in small groups to make sense of the problems or tasks they are solving and the mathematics they are examining.
- Teachers circulating as students work in order to hear their thinking, look over any written work that is being created, and ask the kinds of questions that support and deepen sense making.
- Whole-class discussions that bring together the thinking that emerged as students worked together, including the sharing of written work, for deeper analysis.
- Students providing some kind of written record indicating what they’ve learned during the lesson.

These components provide opportunities for all students to read, write, speak, and listen like mathematicians.

As you view the following videos, watch for the lesson components named above and consider the extent to which you see evidence that students are engaged in disciplinary literacy practices. Also pay attention to the extent to which these components seem to engage *all* students, not just some students, in these practices.

**Video and Reflection:** Watch the lesson in *Collaborating to Extend Mathematical Understanding*, which focuses on triangle congruence theorems and the academic language associated with those theorems. You may want to take notes on the questions below.

**Before you watch:**What structures are you thinking about implementing as a way to engage students in reading, writing, speaking, and listening like mathematicians? What implications are there for how you might structure your mathematics lessons?**Watch the video:**As you watch, note the ways students read, write, think, and talk like mathematicians. How did the structure of the lesson provide students with opportunities to engage in these practices? What is Mr. Boyd’s role in supporting these practices?**Reflect:**What are some ways students were reading, writing, speaking, and listening like mathematicians? How did the structure of the lesson provide all students with opportunities to engage in these practices? How did Mr. Boyd support engagement in these practices*?*

**Video and Reflection**: Now watch *Blended Learning: Using Technology to Learn Math Concepts* and *Learning in a Blended Classroom*, in which the teacher is using technology to facilitate peer-to-peer communication as students work in small groups on problems involving arithmetic sequences. The expectation is that students should be able to explain and teach their solutions to each other. You may want to take notes on the questions below.

**Before you watch:**In what ways do you encourage peer-to-peer communication among your students? How have you used technology to support student engagement?

**Watch the video (**As you watch, note the ways students read, write, speak, and listen like mathematicians. How did the structure of the lesson provide students with opportunities to engage in these practices? How is Mr. Young supporting engagement in these practices? How is technology supporting engagement in these practices?*Blended Learning: Using Technology to Learn Math Concepts)*:**Watch the video (**Again, note the ways students read, write, speak, and listen like mathematicians. How did the structure of the lesson provide students with opportunities to engage in these practices? How is Mr. Young supporting engagement in these practices? How is technology supporting engagement in these practices?*Learning in a Blended Classroom)*:**Reflect:**What are some ways students were reading, writing, speaking, and listening like mathematicians? How did the structure of the lesson provide all students with the opportunity to engage in these practices? How did Mr. Young support engagement in these practices? How did the technology support engagement in these practices?

**Video and Reflection:** Now watch *Talking Like a Mathematician* to see students working collaboratively in small groups and with their teacher to discuss systems of inequalities. You may want to take notes on the questions below.

**Before the video:**What kinds of interactions might you have with students to support their engagement in disciplinary literacy practices? How might a focus on multiple approaches to solving mathematics problems create opportunities for that engagement?**Watch the videos:**As you watch, note the ways students read, write, speak, and listen like mathematicians. How did the structure of the lesson provide students with opportunities to engage in these practices?**Reflect:**What are some ways students were reading, writing, speaking, and listening like mathematicians? How did the structure of the lesson provide all students with the opportunity to engage in these practices? How did Mr. Dinh provide all students with the opportunity to engage in these practices?

Designing mathematics lessons that support and strengthen student engagement in disciplinary literacy practices and provide opportunities to engage in the authentic mathematical activity articulated in the CCSSM will mean thinking carefully about how lessons are planned and structured. Consider these Mathematics Teaching Practices identified by NCTM (2014), which represent a core set of high-leverage practices informed by recent research and intended to strengthen mathematics teaching and learning, particularly given the expectations of the CCSSM.

**Reflect: **Read the CCSSM Mathematics Teaching Practices [PDF] according to the instructions below.

- On the first read, think about how these connect to your own experiences as a mathematics teacher. Highlight in pink any aspects of the text that make these connections for you.
- On the second read, select two to three Mathematics Teaching Practices and think about how they connect to disciplinary literacy in mathematics, including reading, writing, thinking, and speaking. Also think about the extent to which you saw these practices reflected in the videos you’ve observed. Highlight in yellow any aspects of the text that makes these connections for you.
- On the third read, revisit the same two to three Mathematics Teaching Practices and think about the extent to which you currently engage in these practices and what aspects of these practices you want to strengthen. Highlight in green any aspects of the text that make these connections for you.

Increasingly, resources are becoming available to help you structure and plan mathematics lessons that engage students in disciplinary literacy practices while also incorporating these Mathematics Teaching Practices that are designed to strengthen mathematics teaching and learning in ways that address the expectations of the CCSSM. Go to Resources at the end of this unit to see a list.

One important question to consider is how mathematics lessons might be structured. How might they begin? How might they end? What happens in the middle? It is clear that structuring lessons around rich non-routine mathematics problems and tasks is important, because solving these kinds of problems and tasks is at the heart of authentic mathematical activity. These kinds of problems and tasks provide opportunities for students to share and discuss ideas, clarify understandings, develop convincing arguments, learn to see things from other perspectives, and develop a language for communicating about their mathematical thinking (Smith et al., 2009). In* Thinking Through a Lesson: Successfully Implementing High-Level Tasks* (Smith et al., 2008), the following structure is offered for lessons that have rich non-routine mathematics problems and tasks at their core:

Part 1: Select and set up a mathematics problem or task.

Part 2: Support students’ exploration of the problem or task.

Part 3: Share and discuss the task.

This lesson structure has important implications for planning. Below are three aspects of planning a lesson with a rich non-routine mathematics problem or task at its core.

First, identify the kinds of problems or tasks that address the mathematics content that is to be the focus of the lesson. Is the problem one that all students will be able to engage in at some level? Is it rich enough to provide a challenge to students who might need that challenge? Is it likely to elicit rich discussions among your students? Is it aligned with targeted mathematics content and practice standards? This typically involves solving the problem or task in order to think about the range of strategies students might use, what tools and resources they might need, and how you want students to share and record their work.

Secondly, think about the kinds of questions you should be ready to ask during the lesson as students work on the problem. What will help them get started if they are struggling? What will help them focus on the key mathematical ideas? What problem-solving strategies might be helpful? What models or representations might be leveraged? How might you encourage conversation among groups of students so their thinking can be shared? It is useful to identify these kinds of questions before the lesson begins.

Thirdly, identify how you will orchestrate the whole-class discussion of the work that students complete. What strategies and representations will you want students to share, and why? In what order might these best be shared? What important connections do you want to help your students make as they look across the different strategies and representations? How will you help them make the kinds of mathematical generalizations that deepen their mathematical understanding? And how will you build on this lesson in subsequent lessons?

While it can be time-consuming to plan these kinds of lessons, it can be very helpful when it comes to enacting the kinds of lessons that engage students in disciplinary literacy practices that are consistent with the Mathematics Teaching Practices. Over time, you may find that this lesson structure feels increasingly comfortable for you and your students as the classroom culture continues to shift toward the authentic work of mathematicians. You may also find that your students more readily engage in challenging mathematics problems and tasks that reflect the expectations of the CCSSM. Finally, as you become more familiar with the range of materials and resources that are available, and as this lesson structure begins to feel more comfortable, you may find that it takes less effort to plan these kinds of lessons.

While good teaching requires investing time and energy into structuring and planning lessons, it is also important to attend to how lessons unfold, including what students seem to be learning from the lesson you are offering them.

One important consideration is whether the mathematics problems or tasks you identified to be at the center of your lesson actually engage students in the kind of mathematical thinking and reasoning you had intended and whether students are engaging in disciplinary literacy practices as you had hoped.

For instance, researchers (e.g., Boston and Smith, 2009; Stein et al., 1996) have found that rigorous non-routine mathematics problems and tasks were often enacted in ways that inadvertently reduced the level of challenge. This can happen when problems or tasks are broken down into a series of steps for students to work through, when the focus is on procedures and answers rather than on the thinking and reasoning behind these procedures and answers. It can also happen if the teacher explains how to solve the problems and tasks before letting students engage in trying to figure them out for themselves. There is a much greater likelihood that students will engage in the kind of thinking that is consistent with the authentic work of mathematicians—and the disciplinary literacy practices they engage in—if mathematics problems and tasks are enacted as intended.

An important implication is that mathematics lessons need to allow students to engage in “productive struggle” if they are to learn the mathematics that is the focus of the lesson and if they are to meaningfully engage in disciplinary literacy practices. What are some indicators of whether this is happening during your mathematics lesson? *Principles to Actions: Ensuring Mathematical Success for All *(NCTM, 2014, p. 49) identifies the following classroom-based indicators of success specifically focused on this productive struggle:

- Students are engaged in the tasks and do not give up. The teacher supports students when they are “stuck” but does so in a way that keeps the thinking and reasoning at a high level.
- Students explain how they solved a task and provide mathematical justifications for their reasoning.
- Students question and critique the reasoning of their peers and reflect on their own understanding.
- Students are able to use tools to solve tasks that they cannot solve without them.
- Students explain their thinking about a task to their peers and the teacher. The teacher asks probing questions based on the students’ thinking.

These indicators are consistent with what can be seen in the instructional practice guides on the Achieve the Core website as well as what is captured in many of the videos now available to show what this mathematics teaching practice looks like in action.

A second important implication is that students should be producing work, either during the lesson or at home, that provides evidence of the kind of thinking and reasoning you hope to support and the kind of disciplinary literacy practices you plan to address. What do you see in the work you collect from your students? Do you see evidence of students persisting in the solution of rigorous problems and tasks? Do you see evidence of students explaining their thinking and reasoning? Are you providing students with feedback in ways that support their reengagement with the content so they have opportunities to strengthen that work? To what extent are there opportunities for students to share, discuss, and revise this written work as part of your lesson?

Strengthening one’s mathematics teaching practice in ways that incorporate disciplinary literacy practices may not happen overnight, even with the best of resources, particularly since many of these practices may be new and unfamiliar to both you and your students. What are some strategies for beginning to make some of the changes to your mathematics teaching practice that you may now feel are important to incorporate? What are some strategies for strengthening some of the approaches that may already be in place to some degree but need further development? As you might guess, working together with colleagues, rather than working alone, is an important strategy for successfully incorporating disciplinary literacy practices into one’s ongoing mathematics instruction.

Here are some suggestions for how to work with your middle school or high school mathematics team to examine and discuss incorporating disciplinary literacy practices into your ongoing mathematics instruction:

- Planning and reflecting on mathematics lessons in grade-level teams, course-level teams, or mathematics department teams with the goal of designing lessons that reflect the CCSSM and a range of disciplinary literacy practices
- Collecting, sharing, and discussing student work that is aligned with the expectations of the CCSS and reflects a range of disciplinary literacy practices
- Visiting each other’s classrooms to collect data about student engagement in the CCSS and disciplinary literacy practices and then reflecting together on implications
- Videotaping one’s own mathematics lesson and reviewing the evidence regarding student engagement in the CCSS and disciplinary literacy practices and considering the implications
- Partnering with a colleague or a small group of colleagues to form “video learning teams” (Knight, 2014) to share and discuss videos from each other’s classrooms in order to analyze and strengthen instruction

In many schools and districts, teams of teachers engage in this collaborative and reflective work through professional learning communities (PLCs). Increasingly, tools and resources are becoming available to support these PLC efforts. Several examples are outlined in three resources specifically designed to support the expectations of the CCSS at the secondary mathematics level: *Common Core Mathematics in a PLC at Work, Grades 6–8* (Briars et al., 2012), *Common Core Mathematics in a PLC at Work, High School* (Zimmermann et al., 2012), and *Common Core Mathematics in a PLC at Work, Leader’s Guide* (Lawson and Kanold, 2012). You may find these and other similar resources valuable as you thoughtfully take on the commitment to collaborate with colleagues in ways that support the incorporation of disciplinary literacy practices in your classroom.

It is also important to keep in mind that our professional organizations are eager to provide support as you contemplate shifting and strengthening your mathematics teaching practice in ways that attend to the expectations of the CCSSM and support disciplinary literacy.

The National Council of Teachers of Mathematics (NCTM) is a professional organization with over 60,000 members dedicated to mathematics teaching and learning. The organization hosts regional and national conferences where you can interact with a wide range of colleagues who share many of your own goals and questions. NCTM offers publications, webinars, and interactive institutes; it also produces a number of journals and other publications, many of which have been referenced in this course.

The National Council of Supervisors of Mathematics (NCSM) is another professional organization dedicated to mathematics teachers and mathematics teacher leaders. It, too, hosts national conferences and regional events, offers a number of publications, and provides professional development opportunities through seminars and webinars.

Finally, the Mathematical Association of America (MAA) is a professional organization designed to advance the mathematical sciences and includes mathematics teachers and mathematics educators at the secondary and collegiate levels. It, too, hosts meetings, provides a range of publications, and sponsors a number of competitions for students. The organization also provides resources targeting mathematical communication so that undergraduate mathematics students are fluent in the disciplinary literacy practices needed by both theoretical and applied mathematicians; many would also be relevant for secondary mathematics students. A number of these resources also provide vivid images of what it means to read, write, speak, and listen like mathematicians. It should be noted that the resources of this professional organization are less focused on the CCSSM, which is a K–12 initiative; however, what it offers is very consistent with these efforts.

The materials developed for this course are intended to provide insight into what it means to read, write, speak, and listen like a mathematician; why it is important to engage students in these disciplinary literacy practices; and how you might plan and enact mathematics lessons that attend to the development of these practices in your classroom.

These materials, including videos that show disciplinary literacy in practice and the interactive activities designed to engage you in disciplinary literacy practices, are intended to provide you with opportunities to reflect on and apply disciplinary literacy practices and support your efforts to strengthen mathematics teaching and learning in these ways.

These materials also provide evidence for how engaging students in disciplinary literacy practices is consistent with the expectations of the CCSSM and with what the research indicates about the mathematics teaching practices that support student learning. Students who have opportunities to engage in these disciplinary literacy practices on an ongoing basis will begin to see themselves as capable mathematical thinkers, will demonstrate increasingly powerful mathematical thinking, and will develop the kind of passion for mathematics that will carry them into any number of STEM fields.

Finally, if we as teachers can create opportunities for *more *students to engage in disciplinary literacy practices, we will be better able to provide an increasingly diverse population of students with important opportunities to realize their potential as mathematicians and consider career opportunities in these STEM fields.

While the materials in this course are intended to provide you with a strong set of resources to leverage as you strengthen your mathematics teaching practice, please keep in mind that new resources are continually emerging. We hope this course is just the beginning of an interesting and satisfying journey that will have an impact on how all of your students engage in and build positive relationships with the discipline of mathematics throughout their lives.

Anderson, M. A., & Little, D. M. (2004). On the write path: Improving communication in an elementary mathematics classroom. *Teaching Children Mathematics, 10*(9), 468–472.

Baxter, J. A., Woodward, J., Olson, D., & Robyns, J. (2002). Blueprint for writing in middle school mathematics. *Mathematics Teaching in the Middle School, 8*(1), 52–56.

Boaler, J. (2013). Ability and mathematics: The mindset revolution that is reshaping education. *FORUM, 55*(1).

Borasi, R., Siegel, M., Fonzi, J., & Smith, C. F. (1998). Using transactional reading strategies to support sense-making and discussion in mathematics classrooms: An exploratory study. *Journal for Research in Mathematics Education, 29*(3), 275–305.

Bosse, M. J., & Faulconer, J. (2010, March). Learning and assessing mathematics through reading and writing. *School Science and Mathematics, 108*(1), 8–19.

Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. *Journal for Research in Mathematics Education, 40*(2), 119–156.

Briars, D. J., Asturias, H., Foster, D., Gale, Mardi A., & Kanold, T. D. (2012). *Common Core Mathematics in a PLC at work, grades 6–8*. NCTM: Reston, VA.

Burns, M. (2004). Writing in math. *Education Leadership, 62*(2), 30–33.

Chapin, S. H., O’Connor, C., & Anderson, N. C. (2013). *Classroom discussions in math: A teacher’s guide for using talk moves to support the Common Core and more* (3rd ed.). Sausalito, CA: Math Solutions.

Common Core State Standards Initiative (CCSSI) (2010). *Common Core State Standards for Mathematics.* Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org.

Countryman, J. (1992). *Writing to learn mathematics: Strategies that work*. Portsmouth, NH: Heinemann.

Dweck, C. (2006). *Mindset: The new psychology of success*. New York: Ballentine Books.

Fernsten, L. A. (2007). A writing workshop in mathematics: Community practice of content discourse. *Mathematics Teacher, 101*(4), 273–278.

Horn, I. (2012). *Strength in numbers: Collaborative learning in secondary mathematics.* Reston, VA: NCTM.

Knight, J. (2014). *Focus on teaching: Using video for high-impact instruction.*Thousand Oaks, CA: Corwin.

Lawson, M. R., & Kanold, T. D. (2012). *Common Core Mathematics in a PLC at work, leader’s guide.* Reston, VA: NCTM.

Lynch, S. D., & Bolyard, J. J. (2012). Mathematical discourse in writing. *Mathematics Teaching in the Middle School, 17*(8), 487–492.

National Council of Teachers of Mathematics (2007). *Five “key strategies” for effective formative assessment.* Research brief. Reston, VA: NCTM.

National Council of Teachers of Mathematics (2014). *Principals to actions: Ensuring mathematical success for all*. Reston, VA: NCTM.

Siegel, M., Borasi, R., & Fonzi, J. (1998). Supporting students’ mathematical inquiries through reading. *Journal for Research in Mathematics Education, 29*(4), 378–413.

Shanahan, T., & Shanahan, C. (2008, Spring). Teaching disciplinary literacy to adolescents: Rethinking content area literacy. *Harvard Educational Review, 78*(1), 40–59.

Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. *Mathematics Teaching in the Middle Grades*, *14*(3), 132–138.

Smith, M. S., Hughes, E. K., Engle, R. A., & Stein, M. K. (2009). Orchestrating discussions. *Mathematics Teaching in the Middle Grades, 14*(9), 548–556.

Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. *American Educational Research Journal, 33*(2), 455–488.

Zimmermann, G., Carter, J. A., Toncheff, M., & Kanold, T. D. (2012). *Common Core Mathematics in a PLC at work, high school.* Reston, VA: NCTM.

**Websites**

Math Class Needs a Makeover

In this TED Talk, middle school mathematics teacher Dan Meyer makes a strong argument for mathematics lessons that engage students in solving the kinds of rigorous non-routine mathematics problems and tasks that require them to read, write, speak, and listen like mathematicians. He talks about what it takes to create these kinds of problem-centered mathematics lessons.

Why We Need Common Core Math

On this site, Jo Boaler of Stanford University discusses four ways to strengthen mathematics instruction, including 1) focusing on learning rather than performance, 2) emphasizing multidimensional approaches that support thinking and reasoning, 3) encouraging student engagement in rich tasks with “low floors and high ceilings” that students can take to different levels, and 4) focusing on depth rather than speed. She supports these recommendations with research and student performance data. She provides a number of examples of rich tasks throughout that can be used to support student learning.

The Teaching Channel: Common Core

This site provides video of teachers working with CCSS tools and resources including those available through Achieve the Core, the Partnership for Assessment of Readiness for College and Careers, and the Smarter Balanced Assessment Consortium.

Implementing the Mathematical Practice Standards

This site provides illustrations of the Standards for Mathematical Practice for Grades 5–10 that consist of a mathematics task, a student dialogue based on that task, a mathematical overview that addresses the mathematical thinking and reasoning that arises during the student dialogue, and student materials that can be used to support the use of these tasks in classrooms.

**Recommended Reading**

Thinking Through a Lesson: Successfully Implementing High-Level Tasks by Margaret S. Smith, Victoria Bill, and Elizabeth K. Hughes. This article identifies a *Thinking Through a Lesson Protocol *(TLLP) that can be used to plan task-centered mathematics lessons that place students’ mathematical thinking at the center of instruction. The protocol includes selecting and setting up a mathematical task, supporting students’ exploration of the task, and sharing and discussing the task. It includes a discussion of how to create questions that assess and advance student thinking as they work on these tasks.

Orchestrating Discussions by Margaret S. Smith, Elizabeth K. Hughes, Randi A. Engle, and Mary Kay Stein. This article identifies five practices that constitute a model for effectively using student responses to high-level mathematics tasks during whole class discussions. The five practices include 1) anticipating student responses to challenging mathematics tasks; 2) monitoring students’ work on and engagement with the task; 3) selecting particular students to present their mathematical work; 4) sequencing the student responses that will be displayed in a specific order; and 5) connecting different students’ responses and connecting the responses to key mathematical ideas.

*Classroom Discussions in Math: A Teacher’s Guide for Using Talk Moves to Support the Common Core and More* (3rd ed.)by Suzanne H. Chapin, Catherine O’Connor, and Nancy Canavan Anderson. This resource provides support for strengthening classroom discourse across Grades K–6 as a way to deepen the engagement of all students in the mathematics content they are learning. It identifies “talk moves,” provides guidelines as to how these might be used, and offers videos of teachers and students engaged in these talk moves together. While the focus is on the elementary grades, there are also implications for secondary grades; a version of this book is currently being developed to specifically address secondary mathematics classrooms.

*Strength in Numbers: Collaborative Learning in Secondary Mathematics* by Ilana Horn. This resource provides guidelines for organizing small-group collaborative work in secondary mathematics classrooms. In particular, it identifies guidelines for identifying “groupworthy” tasks, makes recommendations for fostering “positive interdependence” so all students are engaged and learning, discusses the teacher’s role while students are working, and addresses important questions about status and “equitable mathematics teaching.”

Five “Key Strategies” for Effective Formative Assessment. This resource discusses the research on effective formative assessment and makes recommendations regarding how these effective formative assessment strategies play an important ongoing role in mathematics instruction. These have important implications for how lessons are structured and planned.

**Recommended Resources for Rich Mathematics Problems and Tasks**

Dan Meyer’s Three-Act Math Tasks

Dan Meyer provides a collection of “Three-Act Math Tasks” that he describes as “the three acts of a mathematical story.” The first act introduces a mathematical challenge in the form of a central conflict; the second act engages students in overcoming obstacles, looking for resources, and developing new tools as they address the conflict; and the third act involves resolving the conflict and setting up a sequel or extension.

Mathematics Assessment Resource Service (MARS)

The Mathematics Assessment Program (MAP) is a collection of rich non-routine assessment problems and tasks that align with the expectations of the CCSS. It reflects a collaboration between the University of California, Berkeley, and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. The team works with the Silicon Valley Mathematics Initiative and school systems across the US and UK to develop improved assessments.

SERP Poster Problems

This site provides a number of “Poster Problems” addressing grades 6 and 7 mathematics content that are designed to engage students in thinking and reasoning. Included are suggestions for designing mathematics lessons around these kinds of problems, explanations of the rationale for these kinds of approaches, and discussions about how these kinds of problems can be used for “diagnostic teaching” that supports student learning.

Mathalicious

This site contains “real-world” lessons designed to help middle school and high school mathematics teachers address the CCSSM while challenging their students to think critically about the world.

PARCC: Partnership for Assessment of Readiness for College and Careers

This site contains descriptions of the PARCC assessment system, including professional development modules about the PARCC Performance-Based Assessments and End-of-Year Assessments, sample items, practice tests, and links to videos on the Teaching Channel that address how teachers can use these assessments to strengthen their instruction.

Smarter Balanced Assessment Consortium

This site contains a description of the Smarter Balanced Assessment system, including sample items, practice and training tests, and resources such as a digital library on formative assessment available to teachers from member states.

**Recommended Tools and Other Resources**

The Illustrative Mathematics Project

This site provides instructional and assessment tasks aligned to CCSS content and practice standards by grade level, course blueprints and lesson plans, and other print and video resources for mathematics teachers. There are also opportunities for virtual conversations for teachers and teacher leaders around a specific task, called “Task Talks,” as well as a virtual lecture series with monthly presentations addressing such topics as “Incorporating the Mathematical Practices into the Middle and High School Classroom.”

Achieve the Core

This site is full of materials designed to help mathematics teachers understand and implement the CCSS in mathematics and ELA. The site includes rich tasks and assessments with explanations and supporting commentary, sample lessons with annotations, an instructional practice guide intended to support lesson planning and reflection, and resources designed to support reflection on the expectations of the CCSS including readings and a discussion forum.

Inside Mathematics

This site is designed to be a professional resource for mathematics teachers. The site includes CCSS resources that focus on content and practice standards, classroom videos that address these standards, problems of the month, performance assessment tasks, and tools for leadership.

G’Day Math!

This link contains resources collected and created by James Tanton of the St. Mark’s Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He is currently a visiting scholar at the Mathematical Association of America (MAA).

Principles to Actions: Ensuring Mathematical Success for All by NCTM. This resource lays out a set of strongly recommended research-informed principles and actions that are essential to strengthen mathematics teaching and learning for all students. These include planning and implementing effective instruction as described by the eight Mathematics Teaching Practices; developing socially, emotionally, and academically safe environments in which all students feel secure and confident as they engage in mathematics learning; identifying and accessing resources that are aligned with the CCSS; incorporating tools and technology as an everyday part of the mathematics classroom; providing students with descriptive, accurate, and timely feedback including strengths, weaknesses, and next steps; and working collaboratively with colleagues to plan instruction, solve common challenges, and provide mutual support through which collective responsibility for student learning is addressed.

Common Core Mathematics in a PLC at Work, Grades 6–8 by Diane Briars, Harold Asturias, David Foster, and Mardi Gale. This teacher’s guide illustrates how to sustain successful implementation of the CCSSM for grades 6–8. Discover what students should learn and how they should learn it at each grade level. Acquire strategies for addressing the rigor of the grades 6–8 standards, including the unique content around ratios, proportions, and relationships at grades 6 and 7. Get insight into the new expectations for grades 6–8 assessment as well as the readiness required for the high school standards. There is attention to important supports for student engagement in disciplinary literacy practices throughout.

Common Core Mathematics in a PLC at Work, High School by Gwen Zimmerman, John Carter, Timothy Kanold, and Mona Toncheff. How do you help your students demonstrate mathematical proficiency, reflecting the learning expectations of the Common Core State Standards (CCSSM)? This teacher’s guide illustrates how to sustain successful implementation of the CCSSM for high school. Discover what students should learn and how they should learn it, including deep support for the mathematical modeling conceptual category of the CCSSM. Comprehensive and research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency. You’ll also learn how fundamental shifts in collaboration, instruction, curriculum, assessment, and intervention can increase college and career readiness in every one of your students. Extensive tools to implement a successful and coherent formative assessment and RTI response are included. There is attention to important supports for student engagement in disciplinary literacy practices throughout.

Common Core Mathematics in a PLC at Work, Leader’s Guide by Timothy Kanold and Matthew Larson. How do you help your students demonstrate mathematical proficiency reflecting the learning expectations of the Common Core State Standards (CCSSM)? This leader companion to the grade-level teacher’s guides illustrates how to sustain successful implementation of the CCSSM for mathematics. School leaders will discover how to support and focus the work of their collaborative mathematics teams for significant student achievement and improvement. Readers will receive explicit guidance and resources on how to lead and exceed the assessment expectations of the common core. There is attention to important supports for student engagement in disciplinary literacy practices throughout.